Counting Quiver Representations over Finite Fields Via Graph Enumeration

Let $\Gamma$ be a quiver on n vertices $v_1, v_2, ..., v_n$ with $g_{ij}$ edges between $v_i$ and $v_j$, and let $\alpha \in \N^n$. Hua gave a formula for $A_{\Gamma}(\alpha, q)$, the number of isomorphism classes of absolutely indecomposable representations of $\Gamma$ over the finite field \F_q with dimension vector $\alpha$. Kac showed that $A_{\Gamma}(\bm{\alpha}, q)$ is a polynomial in q with integer coefficients. Using Hua's formula, we show that for each non-negative integer s, the s-th derivative of $A_{\Gamma}(\alpha,q)$ with respect to q, when evaluated at q = 1, is a polynomial in the variables $g_{ij}$, and we compute the highest degree terms in this polynomial. Our formulas for these coefficients depend on the enumeration of certain families of connected graphs.Comment: 16 page

Enhancement of collagen deposition and cross-linking by coupling lysyl oxidase with bone morphogenetic protein-1 and its application in tissue engineering

Cultured cell-derived extracellular matrices (ECM)-based biomaterials exploit the inherent capacity of cells to create highly sophisticated supramolecular assemblies. However, standard cell culture conditions are far from ideal given the fact that the diluted microenvironment does not favor the production of ECM components, a circumstance particularly relevant for collagen. An incomplete conversion of procollagen by C-proteinase/bone morphogenetic protein 1 (BMP1) has been proposed to severely limit in vitro collagen deposition. BMP1 also catalyzes the proteolytic activation of the precursor of the collagen cross-linking enzyme, lysyl oxidase (LOX) to yield the active form, suggesting a deficit in cross-linking activity under standard conditions. We hypothesized that the implementation of fibroblast cultures with LOX and BMP1 may be an effective way to increase collagen deposition. To test it, we have generated stable cell lines overexpressing LOX and BMP1 and studied the effect of supernatants enriched in LOX and BMP1 on collagen synthesis and deposition from fibroblasts. Herein, we demonstrate that the supplementation with LOX and BMP1 strongly increased the deposition of collagen onto the insoluble matrix at the expense of the soluble fraction in the extracellular medium. Using decellularization protocols, we also show that fibroblast-derived matrices regulate adipogenic and osteogenic differentiation of human mesenchymal stem cells (MSC), and this effect was modulated by LOX/BMP1. Collectively, these data demonstrate that we have developed a convenient protocol to enhance the capacity of in vitro cell cultures to deposit collagen in the ECM, representing this approach a promising technology for application in tissue engineeringTis work was supported by grants from Ministerio de Economía y Competitividad (Plan Nacional de I+D+I: SAF2012-34916, and SAF2015-65679-R to F.R-P

PEM-West trajectory climatology and photochemical model sensitivity study prepared using retrospective meteorological data

Trajectory and photochemical model calculations based on retrospective meteorological data for the operations areas of the NASA Pacific Exploratory Mission (PEM)-West mission are summarized. The trajectory climatology discussed here is intended to provide guidance for flight planning and initial data interpretation during the field phase of the expedition by indicating the most probable path air parcels are likely to take to reach various points in the area. The photochemical model calculations which are discussed indicate the sensitivity of the chemical environment to various initial chemical concentrations and to conditions along the trajectory. In the post-expedition analysis these calculations will be used to provide a climatological context for the meteorological conditions which are encountered in the field

The Hetu'u Global Network: Measuring the Distance to the Sun Using the June 5th/6th Transit of Venus

In the spirit of historic astronomical endeavors, we invited school groups across the globe to collaborate in a solar distance measurement using the rare June 5/6th transit of Venus. In total, we recruited 19 school groups spread over 6 continents and 10 countries to participate in our Hetu'u Global Network. Applying the methods of French astronomer Joseph-Nicolas Delisle, we used individual second and third Venus-Sun contact times to calculate the distance to the Sun. Ten of the sites in our network had amiable weather; 8 of which measured second contact and 5 of which measured third contact leading to consistent solar distance measurements of 152+/-30 million km and 163+/-30 million km respectively. The distance to the Sun at the time of the transit was 152.25 million km; therefore, our measurements are also consistent within 1sigma of the known value. The goal of our international school group network was to inspire the next generation of scientists using the excitement and accessibility of a rare astronomical event. In the process, we connected hundreds of participating students representing a diverse, multi-cultural group with differing political, economic, and racial backgrounds.Comment: 19 pages; 7 Figures; 1 Table; Accepted for publication in Astronomy Education Review (AER) For more information see http://www.das.uchile.cl/~drodrigu/easter/index_en.htm

Material Dependence of the Wire-Particle Casimir Interaction

We study the Casimir interaction between a metallic cylindrical wire and a metallic spherical particle by employing the scattering formalism. At large separations, we derive the asymptotic form of the interaction. In addition, we find the interaction between a metallic wire and an isotropic atom, both in the non-retarded and retarded limits. We identify the conditions under which the asymptotic Casimir interaction does not depend on the material properties of the metallic wire and the particle. Moreover, we compute the exact Casimir interaction between the particle and the wire numerically. We show that there is a complete agreement between the numerics and the asymptotic energies at large separations. For short separations, our numerical results show good agreement with the proximity force approximation